Chelsea looked to be on the way to a routine victory after Cesc Fabregas opened the scoring after just five minutes at Stamford Bridge, although Palace responded with gusto, Wilfried Zaha leveling matters four minutes later before Christian Benteke put the visitors in front less than 120 seconds later.
And while Chelsea dominated the remainder of the game, they were unable to find a way back to eventually suffer their first home loss since September.
Tottenham would go on to take full advantage of that result, with Mauricio Pochettino’s men earning a 2-0 win over Burnley, with Eric Dier (66) and Son Heung-Min (77) getting the goals in the second-half at Turf Moor.
Meanwhile, Leicester City eased their relegation concerns with a 2-0 victory over Stoke City, Wilfred Ndidid getting the Foxes up and running after 25 minutes before Jamie Vardy doubled the lead two minutes after the break.
Manchester United saw their hopes of a top-four finish dented as they were held to a goalless draw against West Bromwich Albion at Old Trafford, with Jose Mourinho’s men four points adrift of fourth-placed Manchester City, who face Arsenal on Sunday.
Hull City managed to rescue a vital victory in their fight against relegation as they earned a 2-1 win against West Ham at the KC Stadium.
The Hammers took the lead after 18 minutes as Andy Carroll fired home from close range, although the Tigers were back level eight minutes after the restart through Andrew Robertson.
And, with just five minutes remaining the hosts got the winner, Ranocchia grabbing his brace to take Hull level on points with 17th-placed Swansea City, although the Tigers’ poor goal difference means they remain in the relegation zone.
And finally, Sunderland saw their relegation concerns compounded as they suffered a 1-0 defeat against Watford at Vicarage Road, Miguel Britos grabbing the game’s only goal after 59 minutes to drive another nail into the coffin of the rock-bottom Black Cats.
Burnley 0-2 Tottenham Hotspur
Chelsea 1-2 Crystal Palace
Hull City 2-1 West Ham United
Leicester City 2-0 Stoke City
Liverpool 3-1 Everton
Manchester United 0-0 West Bromwich Albion
Watford 1-0 Sunderland